From 2d4cfb52a05b5db66e50f8f8b6943c9c1e8a3eaf Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Fri, 2 Jan 2026 08:09:01 +0300 Subject: [PATCH 1/2] feat(algorithms, arrays, two-sum): two sum input as bst --- algorithms/arrays/two_sum/README.md | 68 ++++++++++++++ algorithms/arrays/two_sum/__init__.py | 45 +++++++++- .../two_sum_4_input_is_bst_example_1.png | Bin 0 -> 100860 bytes .../two_sum_4_input_is_bst_example_2.png | Bin 0 -> 88609 bytes .../two_sum_4_input_is_bst_example_3.png | Bin 0 -> 71169 bytes .../two_sum_4_input_is_bst_solution_1.png | Bin 0 -> 64099 bytes .../two_sum_4_input_is_bst_solution_10.png | Bin 0 -> 119715 bytes .../two_sum_4_input_is_bst_solution_11.png | Bin 0 -> 94424 bytes .../two_sum_4_input_is_bst_solution_12.png | Bin 0 -> 122766 bytes .../two_sum_4_input_is_bst_solution_13.png | Bin 0 -> 101779 bytes .../two_sum_4_input_is_bst_solution_14.png | Bin 0 -> 121256 bytes .../two_sum_4_input_is_bst_solution_2.png | Bin 0 -> 83971 bytes .../two_sum_4_input_is_bst_solution_3.png | Bin 0 -> 89223 bytes .../two_sum_4_input_is_bst_solution_4.png | Bin 0 -> 100696 bytes .../two_sum_4_input_is_bst_solution_5.png | Bin 0 -> 101687 bytes .../two_sum_4_input_is_bst_solution_6.png | Bin 0 -> 126236 bytes .../two_sum_4_input_is_bst_solution_7.png | Bin 0 -> 93421 bytes .../two_sum_4_input_is_bst_solution_8.png | Bin 0 -> 118834 bytes .../two_sum_4_input_is_bst_solution_9.png | Bin 0 -> 100952 bytes algorithms/arrays/two_sum/test_two_sum.py | 83 +++++++++--------- 20 files changed, 153 insertions(+), 43 deletions(-) create mode 100644 algorithms/arrays/two_sum/images/examples/two_sum_4_input_is_bst_example_1.png create mode 100644 algorithms/arrays/two_sum/images/examples/two_sum_4_input_is_bst_example_2.png create mode 100644 algorithms/arrays/two_sum/images/examples/two_sum_4_input_is_bst_example_3.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_1.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_10.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_11.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_12.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_13.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_14.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_2.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_3.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_4.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_5.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_6.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_7.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_8.png create mode 100644 algorithms/arrays/two_sum/images/solutions/two_sum_4_input_is_bst_solution_9.png diff --git a/algorithms/arrays/two_sum/README.md b/algorithms/arrays/two_sum/README.md index da055900..b5b6a601 100644 --- a/algorithms/arrays/two_sum/README.md +++ b/algorithms/arrays/two_sum/README.md @@ -35,6 +35,74 @@ Output: [1,2] Explanation: The sum of -1 and 0 is -1. Therefore index1 = 1, index2 = 2. We return [1, 2]. ``` +--- + +# Two Sum IV - Input Is a BST + +Given the root of a binary search tree and an integer k, determine whether there are two elements in the BST whose sum +equals k. Return TRUE if such elements exist or FALSE otherwise. + +## Constraints + +- The number of nodes in the tree is in the range [1, 10^3]. +- 10^3 <= Node.data <= 10^3 +- root is guaranteed to be a valid binary search tree. +- 10^4 <= k <= 10^4 + +## Examples + +![Example 1](./images/examples/two_sum_4_input_is_bst_example_1.png) +![Example 2](./images/examples/two_sum_4_input_is_bst_example_2.png) +![Example 3](./images/examples/two_sum_4_input_is_bst_example_3.png) + +## Solution + +The core intuition behind solving this problem is to use a set to track values encountered during a breadth-first search +of the binary search tree (BST). We calculate each node’s complement (i.e., the difference between k and the node’s value) +and check if this complement already exists in the set. If it does, it means there is another node in the BST whose value, +when added to the current node’s value, equals k, and we return TRUE. Otherwise, we add the current node’s value to the set. +If no two nodes with the required sum are found by the end of the traversal, we return FALSE. + +Using the intuition above, the solution can be implemented as follows: + +1. If the BST is empty, return FALSE. +2. Define a set, seen, to store the visited node values. +3. Define a queue, q, to perform the level-order traversal of the BST. + - Enqueue root to q to start the traversal from the root node. +4. While the queue is not empty, repeat the following steps: + - Dequeue a node from the front of the queue. + - Check if the complement of the current node’s value exists in the seen set. If yes, return TRUE. + - Add the current node’s value to the seen set. + - Enqueue its left and right children. +5. If no two nodes with the required sum are found, return FALSE. + +Let’s look at the following illustration to get a better understanding of the solution: + +![Solution 1](./images/solutions/two_sum_4_input_is_bst_solution_1.png) +![Solution 2](./images/solutions/two_sum_4_input_is_bst_solution_2.png) +![Solution 3](./images/solutions/two_sum_4_input_is_bst_solution_3.png) +![Solution 4](./images/solutions/two_sum_4_input_is_bst_solution_4.png) +![Solution 5](./images/solutions/two_sum_4_input_is_bst_solution_5.png) +![Solution 6](./images/solutions/two_sum_4_input_is_bst_solution_6.png) +![Solution 7](./images/solutions/two_sum_4_input_is_bst_solution_7.png) +![Solution 8](./images/solutions/two_sum_4_input_is_bst_solution_8.png) +![Solution 9](./images/solutions/two_sum_4_input_is_bst_solution_9.png) +![Solution 10](./images/solutions/two_sum_4_input_is_bst_solution_10.png) +![Solution 11](./images/solutions/two_sum_4_input_is_bst_solution_11.png) +![Solution 12](./images/solutions/two_sum_4_input_is_bst_solution_12.png) +![Solution 13](./images/solutions/two_sum_4_input_is_bst_solution_13.png) +![Solution 14](./images/solutions/two_sum_4_input_is_bst_solution_14.png) + +### Time Complexity + +The algorithm’s time complexity is O(n), where n is the number of nodes in the binary search tree. + +### Space Complexity + +The algorithm’s space complexity is O(n), as the size of the set can grow up to at most n. + +--- + ## Related Topics - Array diff --git a/algorithms/arrays/two_sum/__init__.py b/algorithms/arrays/two_sum/__init__.py index 6b79adc2..da42e092 100644 --- a/algorithms/arrays/two_sum/__init__.py +++ b/algorithms/arrays/two_sum/__init__.py @@ -1,4 +1,6 @@ -from typing import List +from typing import List, Deque, Set +from collections import deque +from datastructures.trees.binary.node import BinaryTreeNode def two_sum(numbers: List[int], target: int) -> List[int]: @@ -59,3 +61,44 @@ def two_sum_with_pointers(numbers: List[int], target: int) -> List[int]: first_pointer += 1 else: last_pointer -= 1 + return [] + + +def two_sum_find_target(root: BinaryTreeNode, k: int) -> bool: + """ + Checks if two nodes in the binary search tree add up to the given target number + + Args: + root (BinaryTreeNode): root of the binary search tree + k (int): target number + Returns: + bool: True if there are two nodes in the binary search tree that add up to the target, False otherwise + """ + if not root: + return False + + # store the seen values so far during the traversal + seen: Set[int] = set() + + # Keep track of visited nodes, we start with the root node. 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b/algorithms/arrays/two_sum/test_two_sum.py index 0584f72f..09b08070 100644 --- a/algorithms/arrays/two_sum/test_two_sum.py +++ b/algorithms/arrays/two_sum/test_two_sum.py @@ -1,56 +1,55 @@ import unittest -from . import two_sum, two_sum_with_pointers +from typing import List +from parameterized import parameterized +from datastructures.trees.binary.node import BinaryTreeNode +from algorithms.arrays.two_sum import ( + two_sum, + two_sum_with_pointers, + two_sum_find_target, +) + +TWO_SUM_TEST_CASES = [ + ([2, 7, 11, 15], 9, [1, 2]), + ([2, 3, 4], 6, [1, 3]), + ([-1, 0], -1, [1, 2]), +] + +TWO_SUM_TWO_POINTERS_TEST_CASES = [ + ([2, 7, 11, 15], 9, [0, 1]), + ([2, 3, 4], 6, [0, 2]), + ([-1, 0], -1, [0, 1]), +] + +TWO_SUM_INPUT_BST_TEST_CASES = [ + ([7, 3, 13, 2, 5, None, 19], 18, True), + ([8, 4, None, 0, None, -11], 4, True), + ([1, None, 2, None, 3, None, 4], 5, True), + ([900], 900, False), + ([0, -200, 500, -300, -100, 400, 600], 500, True), +] class TwoSumTestCase(unittest.TestCase): - def test_1(self): - """numbers = [2,7,11,15], target = 9""" - numbers = [2, 7, 11, 15] - target = 9 - expected = [1, 2] + @parameterized.expand(TWO_SUM_TEST_CASES) + def test_two_sum(self, numbers: List[int], target: int, expected: List[int]): actual = two_sum(numbers, target) self.assertEqual(expected, actual) - def test_2(self): - """numbers = [2,3,4], target = 6""" - numbers = [2, 3, 4] - target = 6 - expected = [1, 3] - actual = two_sum(numbers, target) - self.assertEqual(expected, actual) - - def test_3(self): - """numbers = [-1,0], target = -1""" - numbers = [-1, 0] - target = -1 - expected = [1, 2] - actual = two_sum(numbers, target) - self.assertEqual(expected, actual) - - -class TwoSumWithPointersTestCase(unittest.TestCase): - def test_1(self): - """numbers = [2,7,11,15], target = 9""" - numbers = [2, 7, 11, 15] - target = 9 - expected = [0, 1] + @parameterized.expand(TWO_SUM_TWO_POINTERS_TEST_CASES) + def test_two_sum_with_two_pointers( + self, numbers: List[int], target: int, expected: List[int] + ): actual = two_sum_with_pointers(numbers, target) self.assertEqual(expected, actual) - def test_2(self): - """numbers = [2,3,4], target = 6""" - numbers = [2, 3, 4] - target = 6 - expected = [0, 2] - actual = two_sum_with_pointers(numbers, target) - self.assertEqual(expected, actual) + @parameterized.expand(TWO_SUM_INPUT_BST_TEST_CASES) + def test_two_sum_input_bst(self, numbers: List[int], target: int, expected: bool): + root = BinaryTreeNode(numbers[0]) + for data in numbers[1:]: + if data is not None: + root.insert_node(data) - def test_3(self): - """numbers = [-1,0], target = -1""" - numbers = [-1, 0] - target = -1 - expected = [0, 1] - actual = two_sum_with_pointers(numbers, target) + actual = two_sum_find_target(root, target) self.assertEqual(expected, actual) From 3c1351ccdfebe6e036730dd672d442c5f84e8f55 Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Fri, 2 Jan 2026 08:21:00 +0300 Subject: [PATCH 2/2] refactor(algorithms, arrays, two-sum): enqueue nodes if present --- algorithms/arrays/two_sum/__init__.py | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/algorithms/arrays/two_sum/__init__.py b/algorithms/arrays/two_sum/__init__.py index da42e092..cec31c78 100644 --- a/algorithms/arrays/two_sum/__init__.py +++ b/algorithms/arrays/two_sum/__init__.py @@ -97,8 +97,10 @@ def two_sum_find_target(root: BinaryTreeNode, k: int) -> bool: seen.add(curr.data) # enqueue the left and right children of the current node - queue.append(curr.left) - queue.append(curr.right) + if curr.left: + queue.append(curr.left) + if curr.right: + queue.append(curr.right) # if we reach here, we have not found two nodes that add up to the target return False

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